On regularity and stability for nonlocal pseudo-parabolic equations involving time-varying delays

We study a class of nonlocal pseudo-parabolic equations with Sonine kernels, where the nonlinearity involves time-varying delays. Our main goal is to address some qualitative questions including the solvability, stability and the Hölder regularity for mild solutions. In addition, we show a result on the convergence of solutions to ones of corresponding subdiffusion equations. The main ingredients for our analysis are regularity estimates of resolvents, a nonlocal Halanay inequality, the fixed point argument and the embedding of fractional Sobolev spaces.